Fourier series for the total electrostatic energy

2 Fourier Series for the Total Electrostatic Energy The Coulombic electronic energy of a continuous charge distribution is defined as 

The integration can be performed in reciprocal space, like the reciprocal-space evaluation of the electrostatic potential discussed in chapter 8. According to Parseval s rule (discussed in chapter 5), 

For the periodic crystal, the integral is replaced by a summation. With Eq. (8.16) for d (H), we obtain 

Expression (9.15) gives the total electrostatic energy and not the cohesive energy of a molecular crystal. It ignores the quantum-mechanical nature of the charge distribution an electron cannot interact with itself, but just such a self-energy is included in the expression. 

---